Jehangir Ratanji Dadabhoy Tata, the group’s former head with a legendary status among India’s businessmen, founded India’s first airline, Tata Aviation Service. He piloted its first commercial flight on Oct. 15, 1932–from Karachi to Mumbai in a single-engine Puss Moth aircraft.

The government nationalized Tata Aviation in 1953 and renamed it Air India. The Tatas never played an active role in aviation since, though its recently retired chairman Ratan Tata had said that returning to the sector was one of his dreams.

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That dream may soon become a reality.

Wednesday, Malaysian discount carrier AirAsia Bhd said it has sought India’s permission to set up a low-cost airline in India in a joint venture with Tata Sons Ltd. and another local investor, Arun Bhatia of Telestra Tradeplace Pvt. Ltd.

Tata Sons, the holding company of the Tata Group, will have a minority 30% stake in the proposed joint venture and won’t have any operational control in it. Still, it could break the $100-billion-revenue salt-to-software group’s airline jinx under its new chairman, Cyrus Mistry.

The group tried, unsuccessfully, at least twice in the past to reenter the business.

After India opened the aviation sector to private companies in 1990s, the Tata Group tried to launch an airline jointly with Singapore Airlines Ltd. In a 2011 interview with The Wall Street Journal, Mr. Ratan Tata, a qualified pilot himself, said the aviation ministry held up his application for years despite constant prodding.

In 1998, after seven years of government inaction, he withdrew the application.

The group tied up again with Singapore Airlines to bid for Air India when the government proposed to sell it in 2001. The Singaporean airline later ended the pact, citing political opposition in India, and the government never sold its stake in the national carrier.

Meanwhile the group expanded its operations globally, buying Anglo-Dutch steelmaker Corus in 2007 and the marquee auto brands of Jaguar and Land Rover the following year. It also acquired the Tetley tea brand and is currently pursuing a bid to buy U.S.-listed hotels group Orient-Express Hotels Ltd.

According to business historian Gita Piramal, the Tata Group’s attempts to invest in the aviation industry show it is “emotional” toward the sector.

Its latest effort comes at a time the local aviation industry is hit by high operational expenses. The cost of financing debt taken by airlines to expand operations in the second half of the last decade, when the market was growing fast, is further hurting the financial performance of companies.

Air India, for instance, hasn’t made a profit since 2007 Kingfisher Airlines Ltd., the most aggressive local airline to expand operations until a couple of years ago and which has now run out of cash, grounded its flights last October.

But low-cost airlines such as InterGlobe Aviation Ltd.’s Indigo and SpiceJet Ltd. are profitable and this may be one of the reasons for AirAsia and the Tata Group to consider the investment.

“We have carefully evaluated developments in India over the last few years and strongly believe that the current environment is perfect to introduce AirAsia’s low fares, which stimulate travel and grow the market,” Tony Fernandes, AirAsia’s founder and group chief executive, said in press statement Wednesday.

But, then Tata’s bid with AirAsia may face the same regulatory hurdles which thwarted one of its previous efforts.

“There is no clarity from the government on issue of new licenses, so we can’t be sure how long the airline may take to actually fly,” said Kapil Kaul, the South Asia chief executive at aviation consultancy CAPA-Centre for Aviation.

Mr. Kaul said the Tata Group’s plan to only invest in, but not to operate, the proposed airline is “surprising.”

Mrs. Piramal, the business historian, says the airline venture is unlikely to become a major milestone for the group. “But, Cyrus Mistry may soon have to learn the art of flying.”

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India Real Time offers analysis and insights into the broad range of developments in business, markets, the economy, politics, culture, sports, and entertainment that take place every single day in the world’s largest democracy. Regular posts from Wall Street Journal and Dow Jones Newswires reporters around the country provide a unique take on the main stories in the news, shed light on what else mattered and why, and give global readers a snapshot of what Indians have been talking about all week. You can contact the editors at indiarealtime(at)wsj(dot)com.